Environmental Engineering Reference
In-Depth Information
The solution of this differential equation is:
⎤
⎥
2
2
a
a
mv
z
=−
α
with
α
=
+
[4.47]
2
b
b
⎥
⎥
b
Fb
=
α
⎦
Numerical example
V
= 5 m
3
Spherical boulder:
m
= 12.5
t
v
= 1.06 m
Impact velocity:
v
= 20 m/s
E
= 2,500 kJ
Embankment
Type l
Type II
Type III
Condition
compacted
average
loose
c
(Poncelet)
0.05
0.10
0.20
M
, [kN/m
2
]
25,000
5,000
1,000
φ
40°
35°
30°
Penetration
z
[m]
z
[m]
z
[m]
Poncelet
0.35
0.71
1.42
Hertz
0.44
0.85
1.62
Habib
0.31
0.65
1.17
Dynamic force
F
[kN]
F
[kN]
F
[kN]
Poncelet
14,300
7,000
3,500
Hertz
11,200
5,900
3,100
Habib
8,600
4,600
2,900
The orders of magnitude of
z
and
F
are comparable, taking into account the
estimated hypotheses on the geotechnical characteristics of the three types of
embankment and in spite of completely different considerations.
